# Lesson Worksheet: Combining Functions Mathematics

In this worksheet, we will practice adding, subtracting, multiplying, or dividing two given functions to create a new function and identifying the domain of the new function.

**Q1: **

What is the domain of the quotient , in terms of the domains of and ? Assume that both domains are subsets of the set of real numbers.

- Athe difference between the domain of and the domain of
- Bthe intersection of the domain of and the domain of
- Cthe larger of the domain of and the domain of
- Dthe union of the domain of and the domain of
- Ethe intersection of the domain of and the domain of

**Q4: **

If and , then find and fully simplify an expression for .

- A
- B
- C
- D

**Q16: **

If where , and where , then find and its domain.

- A,
- B,
- C,
- D,

**Q17: **

If where , and where , find and fully simplify and determine the domain of .

- A,
- B,
- C,
- D,
- E,

**Q18: **

If where , and where , find and the domain of .

- A,
- B,
- C,
- D,
- E,

**Q19: **

If and are two real functions where and , determine the domain of the function .

- A
- B
- C
- D
- E

**Q21: **

Given that and find and state its domain.

- A,
- B,
- C,
- D,
- E,

**Q22: **

If and are two real functions where and , find the domain of the function .

- A
- B
- C
- D
- E

**Q23: **

Given that and are two real functions where and , find the value of if possible.

- A0
- B35
- Cundefined
- D

**Q25: **

If and are two real functions where and , find the value of if possible.

- A
- Bundefined
- C
- D